Results May Vary

I’ve written previously about some of what I consider the shortcomings of orthodox financial economics. In general, it appears to me that economic theory is largely detached from reality in much the same way astronomy was before Copernicus and Galileo.

One instance of this detachment from reality is the “random walk” theory of financial markets. This model of market behavior was developed in the 1960s and still holds sway in the retail research departments of most U.S. brokerage firms. It’s based mainly on this:

What the chart shows is the Dow Jones Industrial Average from its creation in 1896 to the present (monthly closing prices; my apologies for the unreadability). The greenish line is a “linear regression,” that is, the straight line that is the best fit to the actual data points. Linear regression was a cutting-edge tool back in the ’60s, when computing power was rather limited. But there’s an unargued underlying assumption in applying it to a market, which makes the “random walk” theory an exercise in circular logic.

The assumption is that the graph of a stock index like the Dow in a way “wants” to be a straight line but can’t manage it. What economists actually say is that the market “seeks equilibrium,” by which they mean that it wants to go up continuously and at a consistent rate. But instead, there are “perturbations” that cause “fluctuations” above or below the idealized rate of gain. Those fluctuations are by nature random (hence “random walk”) and therefore are unpredictable.

Thus, investors shouldn’t try to guess when the market is going to have one of those “perturbations” – in other words, they shouldn’t try to practice “market timing” – but instead should simply buy stocks and hold them for the long term, because the underlying trend always goes higher. And here the logical circle is closed.

Since the 1980s, the random walk theory has come under increasing criticism, and many economists outside the Wall Street houses acknowledge that it’s not a realistic model. Many still want to cling to some variation of randomness, however, and have developed hybrid models that include some degree of self-recursiveness along with the randomness, giving us things like the exotically named GARCH model: “generalized auto-regression with conditional heteroskedacity.” However, scientific studies have shown that these models have zero value in predicting market movements.

Another argument in favor of “buy and hold” investing is the claim that the stock market consistently over the years has provided an average annual percentage return that is higher than other kinds of investments. But this depends very much on how you calculate the annual return. The usual figure is 8 percent, compared with half that return or less from interest-bearing investments such as bonds.

It’s true that if you take the closing price of an index like the Dow on a given day and calculate the percent change from the same day the year before, and you average that calculation over the past 100 years, you’ll get a figure something like that 8 percent number. But the calculation doesn’t bear any resemblance to how people actually invest: You can’t “buy the Dow” every day and sell it a year later.

I’ve constructed a model that I think represents more accurately how people really invest. I had to make some simplifying assumptions, but I believe the result is still more indicative of the kind of average returns investors can expect.

Here’s the idea: Let’s suppose that a worker sets up a program in which he or she invests a set percentage of his or her income each month. This program continues for 30 years, at which point the worker retires and cashes out. I’ve also assumed that the worker gets a cost-of-living raise at the beginning of each year, based on the nominal inflation rate (based on the Consumer Price Index) for the previous year. (That’s something few workers are actually seeing today, so the model may actually overstate the investor’s returns somewhat.)

The following chart shows the average annual return a worker would have received by following this investment strategy:

The time scale (if you can read it; right-click to open it bigger in a new window) indicates the date upon which the worker began the monthly investment program, and the vertical scale shows the percentage return at the end of 30 years for a worker who started investing on the date shown. For example, a worker who started an investment program in the very first month that Charles Dow calculated his industrial average in 1896 (i.e., the very beginning of the blue line) would have earned an average annual return of 2.86 percent over the next 30 years.

The very highest average return, 18.11 percent, would have been earned by a worker who began a monthly investment program in December 1969 and cashed out in December 1999. Obviously, the average annual return for someone who started 10 years later and cashed out last year would have been quite a bit less, just 3.92 percent at the low point in February 2009.

Worse yet, people who started investing in late 1901 to mid-1903 would have lost money, as would almost everyone who started in 1912. Perhaps most surprisingly, anyone who embarked on this kind of program in the late 1940s to mid-1950s -- which we're used to thinking of as boom times -- would have earned a fairly paltry annual return of about 2 percent or less when they cashed out in the late 1970s-early 1980s -- which were not so booming.

Overall according to this scenario, investors who have cashed out to date have earned an average annual return of 5.05 percent or a median annual return of 4.44 percent. Those figures aren’t all that much above the long-term average or median returns on interest-bearing investments. As I said earlier, the results may overstate the average returns because of my assumption about annual salary increases. In addition, the numbers don’t include any taxes or transaction costs such as brokerage commissions.

However, the real lesson of this exercise isn’t about long-term average returns, it’s about the wide variability of the real-time returns. What it boils down to is that even for a long-term investor, your results still depend entirely on when you start investing and when you cash out. If we relate that to our entry into the career world, it shows how much the decision is out of our hands: We can’t choose what year we’re born. Whether we like it or not, we’re all market-timers.

It Could Be Worse

Today’s economic reports, stock market decline and related news stories were all pretty ugly. But they were 1970s ugly rather than 1930s ugly, which is some consolation.

The Dow Jones Industrial Average is down, as of today’s close, 44 percent from its all-time high set a little over a year ago. The decline from the January 1973 high to the December 1974 low was 45 percent. The decline from the September 1929 high to the July 1932 low was almost exactly twice as much, 89 percent. An 89 percent decline from the October 2007 high would put the Dow at about 1558, so today’s much-discussed close slightly below 8000 may not look quite so bad.

Mathematically, stock market movements resemble earthquakes; that is, they’re fractal and scale according to a power law. In oversimplified English, which is the only way I can understand this kind of thing, what that means is that exponentially larger movements occur exponentially less often than small movements. This is why seismologists are unable to tell Californians exactly when “the Big One” will occur but insist that the more time passes without a big one, the more likely it becomes. So same thing with the stock market.

The current bear market is the second since 2000; the decline from the January 2000 high to the October 2002 low amounted to about 38 percent. From the seismological point of view, that might mean that we’re less likely to get a “big one” of near 90 percent, and instead must suffer through a series of less catastrophic but still thoroughly unpleasant medium-sized shocks.

From the standpoint of technical market analysis, 8000 on the Dow isn’t very interesting anyway. The really interesting number is the October 2002 low at about 7286, which we could stretch a bit down to the 7000 level as an idealized 50 percent decline. If that range doesn’t hold, then we’re potentially looking at a decline to 1.) the 5300-5700 area, representing the trading range of a 1996 pause, for a possible 62 percent drop; the 3600-4000 range, which is the level of a somewhat significant sideways move in 1994 and would amount to a roughly 75 percent decline; or the aforementioned near-90 percent decline to the 1500 range. And of course there's always the possibility that the world could come to an end and the Dow would fall to zero, but personally I give that pretty low odds.

Those are, of course, the worst-case scenarios. The most optimistic case would be that the market is “base-building” right around where it is now and will launch a new, multi-year uptrend from here that will replenish all the 401(k) accounts and other investments that have been stripped in the past year. I’d feel a lot more confident about that scenario if it didn’t depend so much on believing that the same people who contributed so much to the current problems - and who are still apparently more interested in self-justification and self-aggrandizement than in doing anything for their society or their world - will somehow suddenly start making all the right decisions.

Spin Cycle

The big economic news this morning was the report that Germany’s gross domestic product declined in the third quarter, marking the second quarter in a row that Europe’s biggest economy has posted a decline in output. That two-quarter decline of course prompted finance reporters to proclaim that Germany now has met “the technical definition of a recession,” which they said is “two or more quarters of decline in GDP.”

Um, no. In the U.S. at least, the organization that more or less officially declares when recessions begin and end, the National Bureau of Economic Research, defines a recession “technically” like this:

“A recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. A recession begins just after the economy reaches a peak of activity and ends as the economy reaches its trough.”

In practical terms, most recessions do include two or more consecutive quarters of declining GDP, but a recession can start or end during a quarter that shows an overall increase. As the NBER puts it:

“Most of the recessions identified by our procedures do consist of two or more quarters of declining real GDP, but not all of them. The most recent recession in our chronology was in 2001. According to data as of July 2008, the 2001 recession involved declines in the first and third quarters of 2001 but not in two consecutive quarters. Our procedure differs from the two-quarter rule in a number of ways. First, we consider the depth as well as the duration of the decline in economic activity. Recall that our definition includes the phrase, "a significant decline in economic activity." Second, we use a broader array of indicators than just real GDP. One reason for this is that the GDP data are subject to considerable revision. Third, we use monthly indicators to arrive at a monthly chronology.”

So far, the NBER hasn’t declared that the U.S. economy is in a recession, but they’re often a little slow to make such determinations; it wasn’t until July 2003 that they decided the 2001 recession had ended in November of that year.

Interestingly, the NBER body that makes these determinations is called the Business Cycle Dating Committee. Until recently, a casual observer of the talk coming out of Wall Street and Washington might have gotten the idea that the “business cycle” was a thing of the past, there would be no more downturns, just an endless vista of rising prosperity until the end of time, because our god-like regulators and CEOs would exercise their miraculous powers to make it so.

These of course would be the same regulators and CEOs who are now running hysterically around seeking taxpayer handouts and warning of the imminent collapse of our entire economic system if they don’t get them.

Cycles play a large role in the natural order and are often related to the kind of yin-yang/creation-destruction/attraction-repulsion systems found widely in philosophy and physical science. Given the fundamental dualism of financial and economic dynamics (buy or sell), it would be pretty surprising if we didn’t see some evidence of cyclicality in the economy and markets.

Well, no surprise here:



The chart shows the daily closing price of the Dow Jones Industrial Average from 1897 to the present, on log scale (click to enlarge). The gridlines are set to a time interval of three and a quarter years, and as you can see if you look closely, many of the most significant lows in the index occur pretty close to those lines.

That cycle is even clearer in this next one:



What this chart shows is the 52-week average of the daily percentage price change in the Dow over the same period shown in the first chart. The cyclicality in this time series is pretty obvious, though it clearly isn’t precise enough to be useful in making investment forecasts.

Possibly the most interesting thing about this chart is the fact that the Oct. 27 low in the Dow at 8175 came just seven days shy of the exact predicted date for the 3.25-year cycle low. The index and the average rate of change both rebounded from that point, possibly signaling the start of an upswing that could last a year or more. However, for that interpretation to retain any validity, the index will have to stay above the 8175 level; it’s succeeding so far, but just barely.

When Oilmen Ruled the World

As the saying goes, "One picture is worth a thousand words." This one might be worth several thousand (click to enlarge; in case it isn't clear, the light blue line is oil, the darker line is the Dow). What it shows is the cumulative daily percent change in the Dow Jones Industrial Average and the same calculation for New York Mercantile Exchange crude oil futures, from Jan. 22, 2001, through last Tuesday (the most recent date for which the U.S. Department of Energy could provide crude prices).

In other words, the chart shows what an equal investment in the Dow and in oil would have returned on any given day since then, up to last week. Obviously, except for the first three years, oil would have been a much better investment than the stock market. Even after the steep decline from last summer's all-time high (when oil was up a staggering 65 percent while the Dow was up a piddly 9 percent), it's still up 29 percent overall. As of Monday's close, the Dow is down 5.5 percent over the same period.

The significance of the starting date, of course, is that it was the first trading day after George W. Bush was sworn in as president.

No Bull

Observers have been comparing stock market dynamics with Taoist concepts for many years now; Bennett W. Goodspeed’s book, “The Tao Jones Averages,” was published in 1984, for example. It’s a reasonable idea; the longstanding bull and bear symbolism lends itself readily to analogy with the yin and yang of Chinese philosophy.

In the Wall Street mainstream, unfortunately, the current understanding of what constitutes a bull or bear market is pretty superficial. Many analysts and financial journalists insist that a bear market is a decline of 20 percent or more, which is an arbitrary, meaningless and ultimately useless way of looking at the market.

If bull/bear really is equivalent to yin/yang, then there must be fundamental qualitative differences between bull and bear markets; it isn’t just a matter of whether the market is going up or going down. And there are a number of technical analysts who have said just that for many years, arguing that bull markets are structurally different from bear markets, and noting that, for example, a rally can occur within an ongoing bear market without reversing the overall trend.

One example that has been noted fairly widely: Bear markets tend to move faster than bull markets; that is, the market falls by larger increments and in less time than it rises in bull markets. And even a fairly superficial look at the data supplies some confirmation of this view. Using a database of daily closing prices for the Dow Jones Industrial Average from 1896 to the present, the average percentage change on up days has been 0.750 percent, while the average change on down days has been 0.774 percent. On the other hand, 52 percent of all trading days have seen advances, while 47 percent have seen declines, with about a half-percent showing no change.

It occurred to me that there might be a way to use this information as a sort of trend indicator. What I did was compare the 20-day median percent change in the index with the overall average of up days (i.e., 0.750 percent) and the equivalent average for all down days (0.774 percent). Then I plotted all days when the current 20-day median was above the up average or below the down average. Here’s the result, along with the Dow for comparison:



I'm sorry the dates aren't clearer; I'm just learning to use the image upload on this site. But two things jump out from this chart. First, periods when the 20-day average change is above or below the long-term up or down average are fairly rare. Second, we’re in one of those periods right now.

That’s right: Starting on Oct. 10, the 20-day median percent change in the Dow fell below the 118-year average for down days, and it has continued to fall further below it, as of Monday’s close. It’s now about a full percentage point below the long-term average and is at the lowest level since early 1932, during the worst of the fierce 1929-32 bear market.

I don’t know whether this bull/bear indicator has any predictive value, but there is one thing that might be worth noting: In general, the lowest readings on this indicator have coincided with the steepest phases of bear-market declines – NOT with the end of the decline. So even if we were to take an optimistic view that this indicator has reached its lowest point, it still wouldn’t preclude the Dow from falling significantly lower.

Update 4:35 p.m.:

Today's 889-point jump in the Dow had no effect on the bull/bear indicator described above. In general, all it did was carry it back toward the upper end of the downward-tending trading range it has been in for the past three weeks.

Also, a little more explanation about the chart above: Ostensibly bullish moves are those above the zero line, shown in red to represent "fiery yang energy," as they say; bearish moves are those below the zero line and are shown in blue, representing "cool, watery yin energy."